Radiation Physics and Chemistry 61 (2001) 537–540

Interaction of photons with some solutions

Kulwant Singh*, Gagandeep Kaur, G.K. Sandhu, B.S. Lark

Department of Physics, Nuclear Spectroscopy Laboratory, Guru Nanak Dev University, Amritsar-143005, India

Abstract

The linear attenuation coefficients in aqueous solutions of some chlorides and sulphates, viz. MgCl2 � 6H2O, CaCl2,SrCl2 � 6H2O, BaCl2 � 2H2O, Na2SO4, K2SO4 and MgSO4 � 7H2O were determined at 81, 356, 511, 662, 1173 and

1332 keV by the g-ray transmission method in a good geometry setup. From the precision measured densities of thesesolutions, mass attenuation coefficients were then obtained which varied systematically with the corresponding changesin the concentrations (g/cm3) of these solutions. A comparison between experimental and theoretical values of

attenuation coefficients has shown that the study has potential application for the determination of attenuationcoefficients of solid solutes from their solutions without obtaining them in pure crystalline form. r 2001 ElsevierScience Ltd. All rights reserved.

Keywords: Attenuation coefficients; Aqueous solution; Solvent; Salts

1. Introduction

The study of attenuation coefficients is potentiallyuseful in the development of semi-empirical formula-

tions of high accuracy, possibly along the lines detailedby Jackson and Hawkes (1981). Hubbell (1982) andSeltzer (1993) have compiled mass attenuation coeffi-

cients for a large number of compounds and mixtures ofdosimetric and biological importance. An updatedversion of the attenuation coefficients for elements

having atomic numbers from 1 to 92 and 48 additionalsubstances of dosimetric interest has recently beencompiled by Hubbell and Seltzer (1995). Most of theprevious studies for the determination of these coeffi-

cients have been concerned with crystalline samples inthe solid form. In their pioneer work, Teli et al. (1994)have determined the g-ray attenuation coefficients in

dilute solutions of magnesium chloride. Gerward (1996)has determined linear and mass attenuation coefficientsin the general case as well as in the limit of extreme

dilution and in this way developed the theory of X-rayand g-ray attenuation in solutions.

As a sequel to our previous study (Singh et al., 1998;

Gagandeep et al., 2000) on the absorption properties ofsome solutes in water at different concentrations, theattenuation coefficients of MgCl2 � 6H2O, CaCl2,

SrCl2 � 6H2O, BaCl2 � 2H2O, Na2SO4, K2SO4 andMgSO4 � 7H2O at six different g-ray energies in anaqueous medium as a function of concentration are

reported in this paper. Densities which have beenexperimentally determined, are required for the estima-tion of these mass attenuation coefficients.

2. Theory

According to the Beer–Lambert’s law, a narrow beam

linear attenuation coefficient m (cm@1), is given by thefollowing relation:

I ¼ I0e@mx ð1Þ

where I0 and I are the incident and transmitted photon

intensities, respectively, and x the thickness of thematerial. A coefficient more accurately characterizing agiven solution is the density-independent mass attenua-

tion coefficient m=r (cm2/g).

I ¼ I0e@ðm=rÞrx: ð2Þ

*Corresponding author. Tel.: +91-183-258840; fax: +91-

183-258819.

E-mail address: k thind@yahoo.com (K. Singh).

0969-806X/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 9 6 9 - 8 0 6 X ( 0 1 ) 0 0 3 2 5 - 5

Table 1

Mass attenuation coefficients of aqueous solutions of some compoundsa

Solution Density of

the solution

(g/cm3)

Conc.

(g/cm3)

Mass attenuation coefficient m=r (cm2/g)

81 keV 356 keV 511 keV 662 keV 1173 keV 1332 keV

Magnesium chloride

MgCl2 � 6H2O

1.021200 0.05 a 0.184 0.110 0.095 0.085 0.065 0.061

b 0.184 0.111 0.096 0.086 0.065 0.061

1.042107 0.10 a 0.185 0.110 0.095 0.085 0.064 0.060

b 0.186 0.111 0.095 0.085 0.065 0.061

1.064453 0.15 a 0.186 0.110 0.095 0.085 0.064 0.060

b 0.187 0.110 0.095 0.085 0.065 0.061

1.083726 0.20 a 0.187 0.110 0.095 0.084 0.064 0.060

b 0.188 0.110 0.095 0.085 0.065 0.061

1.100204 0.25 a 0.188 0.109 0.094 0.084 0.064 0.059

b 0.189 0.110 0.095 0.085 0.065 0.060

Calcium chloride

CaCl2

1.035680 0.05 a 0.187 0.110 0.095 0.085 0.065 0.061

b 0.188 0.111 0.095 0.085 0.065 0.061

1.072139 0.10 a 0.192 0.110 0.095 0.085 0.064 0.060

b 0.193 0.110 0.095 0.085 0.065 0.061

1.108080 0.15 a 0.197 0.109 0.094 0.084 0.064 0.060

b 0.198 0.110 0.095 0.084 0.064 0.060

1.141173 0.20 a 0.201 0.109 0.094 0.084 0.064 0.060

b 0.202 0.109 0.094 0.084 0.064 0.060

1.184648 0.25 a 0.205 0.108 0.094 0.084 0.064 0.060

b 0.206 0.109 0.094 0.084 0.064 0.060

Strontium chloride

SrCl2 � 6H2O

1.050231 0.05 a 0.203 0.110 0.095 0.085 0.065 0.061

b 0.204 0.111 0.096 0.085 0.065 0.061

1.077728 0.10 a 0.222 0.110 0.095 0.085 0.064 0.060

b 0.222 0.111 0.095 0.085 0.065 0.061

1.096837 0.15 a 0.239 0.110 0.095 0.085 0.064 0.060

b 0.240 0.111 0.095 0.085 0.064 0.060

1.124722 0.20 a 0.255 0.110 0.095 0.084 0.064 0.060

b 0.255 0.110 0.095 0.084 0.064 0.060

1.190348 0.25 a 0.269 0.110 0.094 0.084 0.063 0.059

b 0.270 0.110 0.095 0.084 0.064 0.060

Barium chloride

BaCl2 � 2H2O

1.031267 0.05 a 0.290 0.115 0.099 0.088 0.067 0.062

b 0.291 0.115 0.099 0.088 0.067 0.063

1.067021 0.10 a 0.397 0.120 0.102 0.090 0.069 0.064

b 0.397 0.120 0.102 0.091 0.069 0.064

1.105524 0.15 a 0.502 0.125 0.105 0.093 0.071 0.066

b 0.502 0.125 0.106 0.094 0.071 0.066

1.137737 0.20 a 0.602 0.129 0.108 0.096 0.072 0.068

b 0.603 0.130 0.109 0.096 0.072 0.068

1.172951 0.25 a 0.702 0.134 0.111 0.098 0.074 0.070

b 0.703 0.1341 0.112 0.099 0.074 0.070

Sodium sulphate

Na2SO4

1.0410180 0.05 a 0.182 0.111 0.095 0.085 0.065 0.061

b 0.183 0.111 0.096 0.085 0.065 0.061

1.0818457 0.10 a 0.182 0.109 0.095 0.085 0.064 0.061

b 0.184 0.110 0.095 0.085 0.065 0.061

1.1264854 0.15 a 0.181 0.109 0.094 0.084 0.064 0.060

K. Singh et al. / Radiation Physics and Chemistry 61 (2001) 537–540538

For a binary mixture, the mass attenuation coefficient ofthe solution is given by the mixture rule:

mr¼

mr

� �W

þmr

� �S

@mr

� �W

� �wS ð3Þ

where ðm=rÞs and ðm=rÞw are the mass attenuation

coefficients of the solute and water, respectively, wS theweight fraction of the solute and r the density of thesolution (g/cm3).

A plot of m=r versus wS gives a straight line with theintercept ðm=rÞW and slope ½ðm=rÞs@ðm=rÞW�. The valueof the slope may then be used to calculate the mass

attenuation coefficient of the solid solute.

3. Experimental details

The experimental setup was similar to the one used inour earlier paper (Singh et al., 1998). Radioactivesources 137Cs, 60Co, 133Ba and 22Na of strength 5 mCi

each, were obtained from the Bhabha Atomic ResearchCentre, Trombay, Bombay, India. A 1.5� 5 in. NaI(Tl)crystal having an energy resolution of 12% at 662 keVwas used for the measurement of attenuation coeffi-

cients. The signal from the detector after a suitableamplification was recorded by means of an EGaGORTEC 4 K MCA plug-in-card coupled to a PC/AT.

The transmitted intensity was measured by gating thechannels at the full-width at half-maximum position ofthe photopeak to minimise the contributions of both

small angle and multiple scattering events to themeasured intensity.

4. Conclusions

The mass attenuation coefficients of some aqueous

solutions in the concentration range of 0.05 to 0.25 g/cm3, are summarised in Table 1. These values have beencompared with the values obtained from the use of theXCOM programme developed by Berger and Hubbell

(1987). The values systematically increase with an

Table 1 (continued)

Solution Density of

the solution

(g/cm3)

Conc.

(g/cm3)

Mass attenuation coefficient m=r (cm2/g)

81 keV 356 keV 511 keV 662 keV 1173 keV 1332 keV

b 0.184 0.110 0.095 0.085 0.064 0.060

Potassium sulphate

K2SO4

1.0365001 0.05 a 0.185 0.110 0.095 0.085 0.065 0.061

b 0.186 0.111 0.096 0.085 0.065 0.061

1.0736203 0.10 a 0.187 0.110 0.095 0.085 0.065 0.060

b 0.189 0.110 0.095 0.085 0.065 0.061

Magnesium sulphate

MgSO4 � 7H2O

1.0212212 0.05 a 0.184 0.110 0.096 0.085 0.065 0.061

b 0.184 0.111 0.096 0.086 0.065 0.061

1.0415675 0.10 a 0.184 0.111 0.095 0.085 0.065 0.061

b 0.185 0.111 0.096 0.086 0.065 0.061

1.0623991 0.15 a 0.185 0.110 0.095 0.085 0.065 0.061

b 0.186 0.111 0.096 0.086 0.065 0.061

a Note: a stands for experimental values, and b stands for theoretical

Fig. 1. Plot of mass attenuation coefficient versus weight

fraction of the solute MgO2 � 6H2O.

K. Singh et al. / Radiation Physics and Chemistry 61 (2001) 537–540 539

increase in the concentration of the solute and agree well

with those obtained from tabulated values. For a givensolution, the slope of m=r as a function of weightfraction of the solute gives practically perfect linear plots

(a typical plot for MgCl2 � 6H2O, has been given as anillustration in Fig. 1). From the slope ½ðm=rÞs@ðm=rÞW�,the mass attenuation coefficient of the corresponding

solute in aqueous solution was obtained. The ðm=rÞSvalues for the salts under study have been reported inTable 2 and are compared with those obtained fromXCOM calculations. The agreement is excellent and the

difference is within the experimental uncertainty. It isexpected that the data presented in this paper will beuseful in view of their importance in medical and

biological applications.

References

Berger, M.J., Hubbell, J.H., 1987. XCOM: photon cross

sections on a personal computer. National Bureau of

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Gagandeep, K., Singh, K., Lark, B.S., Sahota, H.S., 2000.

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Hubbell, J.H., 1982. Photon mass attenuation and energy

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Table 2

Derived values of mass attenuation coefficients of the solutes of alkaline earth chlorides

Solute Density of

the salt (g/cm3)

m=r (cm2/g) values of solid solutes

81 keV 356 keV 511 keV 662 keV 1173 keV 1332 keV

Magnesium chloride

MgCl2 � 6H2O

1.569 a 0.214 0.105 0.090 0.080 0.057 0.053

b 0.213 0.105 0.090 0.081 0.061 0.058

Calcium chloride

CaCl2

2.150 a 0.299 0.099 0.085 0.076 0.057 0.054

b 0.2980 0.099 0.085 0.076 0.057 0.054

Strontium chloride

SrCl2 � 6H2O

1.980 a 0.616 0.105 0.089 0.079 0.057 0.053

b 0.616 0.106 0.089 0.078 0.059 0.055

Barium chloride

BaCl2 � 2H2O

3.097 a 2.259 0.128 0.091 0.077 0.056 0.053

b 2.226 0.127 0.093 0.078 0.055 0.052

K. Singh et al. / Radiation Physics and Chemistry 61 (2001) 537–540540